I got past the subdivide problem. Things look selected but they weren’t, once I really had edges select the action happened.
Back to your problem, see how far this gets you:
Export Collada with triangulate all faces.
Import into Blender
Edit Mode, A to select all.
X to delete, but choose Limited Dissolve.
You now have a pretty good starting point. I think that any remainder lines are due to faces not being exactly coplanar.